ECDSA – Elliptic Curve Digital Signature Algorithm

ECDSA is the elliptic curve version of the Digital Signature Algorithm (DSA). ECDSA was first proposed in 1992 by Scott Vanstone in response to the National Institute of Standards and Technology (NIST) request for public comments on their first proposal for their Digital Signature Standard (DSS). It was accepted in 1998 as an ISO standard (ISO 14888-3), in 1999 as an ANSI standard (ANSI X9.62), and in 2000 as an IEEE standard (IEEE 1363-2000) and FIPS standard (FIPS 186-2). It is also under consideration for inclusion in other ISO standards.

Elliptic curve cryptosystems (ECC) were invented by Neal Koblitz and Victor Miller in 1985. They can be viewed as elliptic curve versions of the older discrete logarithm (DL) cryptosystems in which the prime-order subgroup of non-negative integers is replaced by the group of points on an elliptic curve over a finite field. The mathematical basis for the security of elliptic curve cryptosystems is the computational intractability of the elliptic curve discrete logarithm problem (ECDLP).

As with elliptic curve cryptography in general, the bit size of the public key believed to be needed for ECDSA is about twice the size of the security level, in bits. By comparison, at a security level of 80 bits, meaning an attacker requires the equivalent of about 280 signature generations to find the private key, the size of a DSA public key is at least 1024 bits, whereas the size of an ECDSA public key would be 160 bits. On the other hand, the signature size is the same for both DSA and ECDSA: 4s bits, where s is the security level measured in bits, that is, about 320 bits for a security level of 80 bits.

VOCAL offers a wide range of cryptographic solutions in both hardware and software form factors.